-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4600.3261', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.4666673232256737, -0.8844329309978143], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6548607339452851, 0.7557495743542583], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.5644432188667692, -0.825471896962774], 'algebraic': True, 'analytic_conductor': 21.362310190967847, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [23, [1]]], 'bad_primes': [2, 5, 23], 'central_character': '4600.3261', 'coeff_info': ['x^110 - 1', '0.998369103926136 + 0.0570888108627680*I', '\\\\zeta_{110}'], 'conductor': 4600, 'conductor_radical': 230, 'conjugate': 'dirichlet_L_4600.1941', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^91', 0, 0, 0, 'a^40', 0, 'a^72', 0, 'a^133', 0, 'a^147', 0, 0, 0, 'a^24', 0, 'a^119', 0, 'a^131', 0, 0, 0, 0, 0, 'a^163', 0, 'a^101', 0, 'a^74', 0, 'a^4', 0, 0, 0, 'a^127', 0, 'a^18', 0, 'a^82', 0, 'a^135', 0, 0, 0, 'a^66', 0, 'a^80', 0, 'a^115', 0, 'a^161', 0, 0, 0, 'a^100', 0, 'a^147', 0, 'a^63', 0, 'a^2', 0, 0, 0, 'a^109', 0, 0, 0, 'a^76', 0, 'a^108', 0, 0, 0, 'a^63', 0, 'a^26', 0, 'a^34', 0, 'a^149', 0, 0, 0, 'a^82', 0, 'a^58', 0, 'a^77', 0, 'a^55', 0, 0, 0, 'a^16', 0, 'a^95', 0], 'euler_factors': [[0], [1, 'a^91'], [0], [1, 'a^40'], [1, 'a^133'], [1, 'a^147'], [1, 'a^24'], [1, 'a^119'], [0], [1, 'a^101'], [1, 'a^74'], [1, 'a^127'], [1, 'a^82'], [1, 'a^135'], [1, 'a^66'], [1, 'a^161'], [1, 'a^147'], [1, 'a^63'], [1, 'a^109'], [1, 'a^76'], [1, 'a^108'], [1, 'a^26'], [1, 'a^149'], [1, 'a^58'], [1, 'a^16'], [1, 'a^105']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-4600-4600.3261-r0-0-0', 'leading_term': '0.555088921305458165069159722628+0.816984311139522896003021058520*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/4600/3261', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9877181152556522, 2.0965643312659323, 2.666480280506063, 1.8087619277209486, 0.015417096494950704, -1.017398209506603, -0.38852220105065116, 0.7462800824858353, 0.5218630777026455, -1.0664929338653175, -1.8142011593346221, -0.17262422352996945, 2.185835270986686, 1.9781311854342865, -1.3417280010721133, -4.247394285102978, -3.241358788591625, 0.6182538407182823, 2.9853230057967868, 1.8498506571998348, -0.15917343061098474, 0.061656022045313064, 1.6382995856951956, 1.5326895104056388, -0.37695723914798174, -1.0322564299065573, 0.7521888687746466, 2.0979108336535, 0.5896380497258593, -1.663255273279705, -1.4040148301768913, 0.07082134829856992, -1.43885057669602, -5.882749423289288, -7.825726288055766, -4.090097106459984, 1.2945545193213568, 2.742196794692584, 0.7192413037295056, -0.2749034605576269, 0.7133214025125373, 0.5482629803283936, -1.4649728252427427, -1.970266131882133, 0.2587070199673631, 1.649309893445712, -0.06484272686979721, -1.6910740639564938, -0.267711360118336, 1.1882302916604102, -1.3251836555910081, -5.147925214240191, -4.500164912874153, -0.06721123431072437, 1.7388659654279333, -0.9565857044916327, -2.9232238508903947, -0.9497819680376356, 1.3050827889465684, 0.4634092618480475, -0.9181169953857884, 0.08903176884996566, 1.2411355331053846, 0.08654408351287642, -0.602485057392612, 1.8807224100472726, 3.968243072632102, 1.5292294290408972, -2.0165635369425936, -0.7763113648411664, 3.3573027364713104, 3.754602711273356, 0.4502292892488329, -0.3607925185325547, 2.4438428622323345, 3.3723570286944065, 0.6654861887332266, -0.8852996295958988, 0.8033199471809859, 1.7261940809621428, 0.05233836349549273, -0.6415962212395525, 0.8609303991995436, 0.8386044419936173, -1.1116517531121235, -0.004989669271907921, 4.621652477430203, 5.786822339830618, 0.7061386900614381, -3.6305351196603852, -1.940214049873055, 1.150883631018272, 0.46651398994390303, -0.9257260541354102, 0.8168529649607383, 2.348907944043133, 0.08872114033850542, -2.4328133986455898, -1.4563476171382572, 0.056699017223516335, -0.7984687304715795, -0.7943630414068114, 2.0064482786514626, 2.9824475967168613, 0.028263029258304713, -0.8719181944429102, 3.5290847693258955, 6.524911929894757, 2.9339171933645094, -1.5062580449683387, -0.4997896765139001, 2.2820202164587244, 1.4801290084872614, -0.24333581988964256, 0.8626197013658183, 1.8967047960547487, 0.35110219202146375, -0.02396451551142283, 2.5799599336880794, 3.338100709939084, 0.4512017558915778, -0.683611769643301, 1.62815430718438, 1.5635626416918007, -2.13718983083302, -2.6131065066228047, 1.629942044226408, 2.70187612650542, -2.1901962433303166, -5.425951598650429, -2.85089048488136, 0.06684572502659622, -0.12027597162502268, 0.03840530521998298, 1.27984634891604, -0.05813038292746638, -2.5704631792980583, -1.2238636805849166, 1.9356384546208132, 1.0794356538224559, -1.6550048941376816, -0.7372301854877669, 0.557501827991716, -3.6549680841617347, -8.757251367287633, -6.9138953496638855, -1.418342595506901, 0.013332199815269457, -0.8308534386764077, 1.385006063275892, 3.811733062509232, 2.0148670715318504, -0.44521939582722764, 0.3183272546867473, 0.9768184588261877, -0.5284301672963194, -0.27311199974303685, 1.6592942412711005, -0.4160372316101152, -5.028482757118445, -3.914688687525639, 2.1420774785483996, 3.6756778042924783, -0.19427325743799986, -1.3712338535461, 0.9703235005305751, 0.514409614671359, -1.9801023509250348, -0.8404126223981723, 1.9134434359371837, 0.986806746664554, -0.9982044619764741, 0.24575260320780637, 1.4494157090941326, -0.2512478158551328, -0.8607498340469026, 0.34726370530215134, -2.377995612169758, -7.842196996178988, -6.948458086949998, 0.21783873795397207, 3.4000745131678203, 0.6715969752322686, 0.0763574567040655, 2.7136384549687746, 2.257056096072076, -0.6359384195523989, -0.48727268737546525, 0.8616470332884077, -0.6855182322044785, -1.7013543555736328, 0.753002978489593, 1.7439521218919387, -0.8536889811146022, -1.428939232589694, 0.6836541111375438, -0.6812536144524168, -3.9569273524401907, -1.265800209736243, 4.7036375173575635, 4.208926217674781, -1.076435604976101, -1.9746790910457328, 0.6883061386505027, 0.3247691245671777, -1.3174230204248014, -0.06319183982463424, 0.7980689141664883, -1.0073939342308398, -0.906111479212688, 1.547421158907039, 0.781871661270775, -1.793037484708286, 0.23198533395935625, 3.740073882499938, 1.521651724160116, -2.442670627442518, -1.185987391952389, 0.4754831855109051, -3.3612915709752667, -6.326514596942949, -2.5788312618269655, 1.492777435470354, 0.5998269148880248, -0.5262607613971512, 0.5633994377908697, -0.06539064416338264, -1.5231087362410676, 0.1293051141266676, 1.2966151633494771, -1.8260479598543884, -3.343398759227184, 0.3524434299370559, 1.7644696576780297, -2.225224946954786, -3.21571514314259, 1.0526044283293046, 1.8143079855842505, -2.2976566527273117, -3.0157039699349664, 0.037624905080949685, 0.2308868979940347, -1.0484312740676514, 0.9495709139662054, 2.629266049696671, 0.5370489599444342, -0.5261315346467909, 1.2364619835602355, 0.832104025964687, -0.804573981377834, 1.3556309205498136, 2.6049621691418197, -3.477039072128309, -9.398815282224238, -6.168308566518849, -0.289532500750733, -0.35381249831624484, -1.8662293502635459, 0.007852358256449147, 0.7287803067843455, -0.7885852049550449, 0.8988308738631183, 4.161278693451323, 2.8407159109220808, -0.28713838703587574, -0.05706238732989058, 0.19616119768006196, -1.4845645395223994, 0.1747641758978909, 3.8487659508577505, 1.365688949247803, -4.197836354107646, -2.4193957038693554, 3.6661893841215027, 3.666030586115035, -0.05596822279576229, 0.10978794364292802, 1.1602514817551817, -0.9575643983844669, -1.5038674187147787, 1.0510645592040528, 1.1276213484339852, -0.796689888288063, -0.029217556335372125, 0.10261976219775512, -3.801928209056901, -5.10144004436019, -0.7296035271395649, 1.310803035310568, -0.7391597471578017, 1.227092253518819, 5.973633283292303, 4.234768396257023, -1.1878661653441935, -0.8455346584452397, 2.3754607424479977, 1.2645909445742096, -0.893701989145303, -0.1907986047218457, -0.3599581969374629, -1.418090350970767, 1.0146061139108884, 3.458755789524739, 1.072872877207953, -0.49761456626143263, 2.463688403509679, 2.234271412810105, -3.2081241917707803, -4.29489671276281, -0.026864764886456453, 0.19858248765166772, -2.941391706177213, -1.5033925231640828, 1.4130557556765817, -0.6602631962232228, -2.94408333334695, -0.8025538045767214, 0.6696687423617419, -0.40452218725554656, 0.33965096529606925, 1.0674378921260064, -1.5848666090124777, -1.9269902017358105, 2.5750056181093846, 3.451528198515547, -0.6811906465112925, 0.11507410044631944, 5.594423398381386, 5.25568798662318, 0.37815582724089497, 0.030758573784194505, 1.9076661447281957, 0.2990489089418925, -0.4686457867502576, 2.086868217601486, 1.9445188513832687, -0.9313755019982916, -0.4968782258058198, 1.0476779305789183, -0.68326422158357, -1.2306086306199489, 0.9207826616093189, -0.9669480466849492, -4.994834604655404, -1.9774452478332476, 3.784080195164706, 1.5149837910710717, -3.9859596890554725, -2.8837434492483536, 0.431829235119922, -0.30449886705704976, -0.685849980993364, 1.0593360957278177, 0.28665980381074063, -0.6765295309553292, 2.5911824268130133, 4.538327845731964, 1.2565364786248268, -0.752508442226361, 0.3273865580870183, -0.875987655807945, -1.0573971795561554, 5.198537134196897, 9.23981062767807, 3.4255880229513282, -2.5677290541742295, -0.8718077300926648, 1.1029219074954395, -0.5357034930840396, 0.25564242875985543, 2.6703495861087636, 1.1430193226698722, -0.8594489502170117, 0.35500888697939537, 0.1294184753013732, -1.6801822470980372, 0.19953758433695917, 1.771028134257898, -2.4850453134144517, -5.03943037730321, -0.5088155139517098, 2.1134482331413564, -0.813081969406575, -0.43165350035818617, 3.3612388418362587, 1.8987412484045583, -1.8235446780346065, -0.04369020377270691, 2.609708372418231, 0.7890913814746254, -0.4875186274948348, 0.5093743009849676, -0.6261393690243301, -1.6591184279872617, 0.09481251217426143, -1.4680764496843335, -6.560139339286364, -5.456325181646651, 0.5488784592806288, 0.5994339094779036, -2.7243173648255223, -0.42417276401798026, 2.5891566709036544, 0.049462136636804335, -1.2111513965730603, 2.0069730354092234, 2.2335666221781674, -0.7036607824503455, -0.3910460127896213, 0.6524310428986868, -1.273344027226936, -1.334283069985783, 0.8110104124777064, -0.7733463161300189, -2.980445994918925, -0.727753380081636, -1.023490340154099, -7.020583196930756, -7.569365506868143, -0.16646925644890304, 2.8866769680724795, -0.4227956979238868, -0.7576427521739639, 1.129183878460654, -0.1613862460330529, -0.5071006786273309, 1.9746457931767507, 1.2519521972879661, -1.3112229896381151, 0.2715053531078925, 1.9052577371631572, -0.4458249134198798, -0.9062454400129687, 0.9127248567091387, -1.5605495416615034, -3.609477756121425, 2.2224065387956378, 7.085410240101022, 2.6562644143598675, -1.6600427615320248, 0.6203094674004235, 1.602992588883242, -0.8484441745152137, -0.4309820467254042, 1.0544809410557312, -0.1638437121552394, 0.35306908461246633, 2.5701795270403673, 0.2959117283646161, -2.9268849110232353, -0.8917434211580534, 0.5189935858640249, -2.2273706616413955, -1.3056840281737996, 2.629461183793523, 0.06420113134067727, -4.687725750225243, -1.6473015476212383, 2.985332063146675, 1.0324145556735749, -1.156444144428437, 0.462680613126385, 0.19717943658715803, -1.1415980767908915, 0.9541503748290322, 2.0601658907436646, -0.08012193374370097, 0.3678329119890196, 1.8867128641070559, -0.8701682091412312, -1.3580565962186602, 4.867995032928172, 6.986025732764421, 1.013252613507347, -1.6451854630082543, 1.1301778198329495, 0.7635112002309393, -0.4457650642894847, 3.0326470565312436, 4.592955184203207, 0.7522298675124134, -0.8943841859626535, 0.4750240692942884, -0.7009271791108995, -1.6175713001701513, 0.249661299608254, -0.16629434405525673, -0.9160702494620905, 3.8308941697766103, 6.424108160509748, -0.0882348928916583, -4.7705610536046645, -0.613209900292833, 2.1870612079481058, -0.03926115160232509, 0.5514194469814084, 2.3029513725638395, -0.537588336925843, -2.297986763959274, 0.4671860170080976, 1.021818503704439, -0.7638183563816462, 0.4077016867094636, 0.9103293321811168, -1.5699323388652777, -0.5948479974565556, 2.1151417947354467, -1.1517066094275015, -4.637744835394388, -1.3158350327548323, -0.07616990941888815, -5.213533573417369, -5.409381776898528, 1.0788591766577296, 3.0275377227235234, 0.3091266475211647, 0.020136530432001056, 0.06854741615559518, -0.63023295938956, 2.609426156270114, 5.780210906712601, 2.7621998273777124, -0.2725797488758954, 0.7013454997087253, -0.7391600408660859, -3.200289450532319, -0.015129458910039268, 2.1401048338265456, -2.597595002116793, -3.7931277712486677, 2.5355553256652543, 4.58264158918133, 0.47630159649416476, -0.3433259082740728, 0.7864267147268081, -1.2570615507251448, -1.8233546053245222, 0.2856816579295437, -0.07673490016679886, 0.036618661126817026, 3.6365829688996976, 3.5772134767420605, -0.4283104033550385, 0.46897855592660526, 2.9748173313725195, -0.6893689050696457, -2.9217311501148706, 1.9637895361424862, 3.735124505333031, -0.42412924924476325, -0.6429131388898366, 2.082203128989991, 0.45125133663309563, -0.9170414387020261, 1.6852457026179977, 1.8155992759359154, -0.5370563930565642, -0.0018809683494246322, 0.11711802811567576, -1.6865534429334352, 0.5098874625486207, 2.761065947102986, -2.728209931834673, -7.407634582744972, -3.124747821648591, -0.020874994929422692, -3.3242405848905303, -3.1774080502360986, 0.9476614795696585, 0.7535721210514102, -0.47553963092393825, 1.7606191691284168, 1.353631027084056, -1.7907634640711911, -0.6531421503396828, 1.5788823062425468, 0.016954236137840622, -0.40618251027945784, 0.4253089603776815, -2.563072074665348, -3.40809499707735, 1.8824803283517726, 1.7756970239426855, -6.389627279875018, -8.3580281749206, -2.3038925305229436, 0.281447325617172, 0.06795907732719066, 2.3650668071731697, 2.0170469601361782, -1.530799318404144, -1.077866627462286, 0.8361613766026271, -0.8159131520951712, -0.8713744213903973, 1.3869955697331895, -0.24149448112290914, -1.6065452060282999, 2.2164155067257565, 2.7978114438096195, -1.7277947941362508, -0.6116719956739785, 3.894427802258841, 1.0562401892283744, -3.1686245372976, -0.25454109275360565, 2.1103940798124254, -0.4630568948855411, -0.8665045441093625, 0.5855032427886193, -0.5132970591725996, -0.40712271383341503, 0.5599612675781067, -3.088948107523732, -5.600365662767967, -1.154197142587199, 1.5340562823394635, -0.8686450457093293, 0.23649368702046555, 2.3411851448539833, -2.190013857000414, -5.025685443881357, 0.14081981402384086, 2.570335231162216, -1.1731478656752563, -1.6041706764979506, 0.6094692333376837, -0.5127913579218044, -1.0158484749806143, 0.31256433990754007, -1.4852917215276202, -2.6238317929369743, 0.4707729470070041, 0.60451943817011, -1.9577293805483822, 1.0800548521493345, 3.944815564904196, -1.3469437501732147, -4.8284950535535875, -0.44844343073529186, 1.0754045281586222], 'positive_zeros': ['1.252831555593744971840177671849', '1.97013959312362304870047433458', '2.61658033305745043321232258325', '3.45845344526942105692389659362', '4.26664796312345003580821707651', '5.26357432766809650371843008222', '6.2117835254147697452656374434', '6.5483636593060318415118737316', '7.43935564853232675612957048817', '8.019456744224121405735092918683', '8.82029202242521720007044586977', '9.656424622670550450406509907615', '9.8070265098903446145172528249', '11.16150764323044003491989540555', '12.00145308273759009011829706754', '12.30420490275246952159703591225', '12.91022608399779005766171388392', '13.71912852598233439619246992342', '14.36688358247747045698929482047', '15.03546072888587588027377752144', '15.51580388589442689154871971671', '16.5675947690183176949531941662', '17.10079826519197458144763184672', '17.91186044744224723276544651083', '18.51345843236486150606313752509', '19.04679846721503143706563777386', '19.703432352163634189527059567', '20.115513026910370465469834349596', '21.04970452150080559989449500283', '21.622117910372588260279529290', '22.55139545813011332097525575509', '22.86926964767132960557927505186', '23.82344301078660277255546725213', '24.26027285663043195290249797917', '25.00869431927028147403980355034', '25.46412933537606810362960023903', '26.06981386292615587332273586149', '26.56292928708380708269170443464', '27.53560777396451276457575018642', '28.28897391868535856301926266644', '28.81944166917784048288364057704', '29.27522334494913981797850242973', '30.008115962881039797842175346179', '30.89869986021544308326086763899', '31.031755416269652480534533923737', '31.67116981460129846681791417467', '32.502749509967145591150374758224', '32.902732153594533226052168613566', '33.92195665242882598123795995911', '34.42248059178545053427084980532', '35.225545236227779038962384187258', '35.468239697781660913479544519679', '36.31688969688182361521202816593', '36.56738090101286488666481731352', '37.5493729063087427703916017252', '37.92758931086349278250125716439', '38.57896190828288639875605764791', '39.263525931333283009710464479623', '39.88103238080840189158076337942', '40.92116815182020654173341141863', '41.200791170019336417568109973908', '41.552338490331722606922759100887', '42.18105038114233520033059763070', '42.91881184596119708867578205422', '43.54368189786552470543451078734', '44.1580747865829448702036568007', '44.45895968170554013356873406969', '45.791288597438676544780298375', '45.94225973342470064588360830049', '46.42376433775866059971922318761', '47.40482282805082001123694190109', '47.74984155015474180870823229330', '48.335379859001810133769143319106', '48.79176414398699275975819493827', '49.345734483774776798406799015346', '50.199935447770343600514908487087', '50.92162806610274256906051517270', '51.4329061782037035174082746442', '51.93453640517997708326795170040', '52.58123173688746972072020941914', '53.24392567142795378220788840599', '53.71530141523200593807158166456', '54.33742643826162195880399649390', '54.8748919817950612489762520714', '55.11911003082107169938882277348', '56.24007047529025940654736953082', '56.96178976003054221409634806348', '57.17452989735698554685549456520', '58.04123322479625022945263717525', '58.51940192841828530717683929741', '58.9698204771171466911978468168', '59.60842236507679311112409408142', '60.21988735010819144296813167800', '60.82278655601055266390557277756', '61.18584120508832391625094784825', '61.93725932989220832582943963448', '62.74135964727887654543903235300', '63.344235841786158147089811737105', '63.79757854612082343890440343928', '64.384794325783908933379068350969', '64.846293240144872588817358237018', '65.42613363656788959495970296683', '66.01728497148795316558199855771', '66.545299413968107302203426575168', '67.28509365432501453001582645592', '67.93979856067780841318732101413', '68.20128849802697233473059672262', '69.21836132038556238985874064526', '69.780349207414524841015523203338', '70.1651755314034952765728311081', '70.61404799793126224433892806964', '71.23455135856466648968225619954', '71.72665180859267238826541111694', '72.47419879131794269199360730322', '72.97168111731109149311040925033', '73.675698465664301148449364510310', '74.20997432229052784610994900587', '74.995118424720712452026271156981', '75.3541669917786113356025481739', '75.83580544024549956559534028917', '76.631251257693389661143974279561', '76.98603789596931724466620072248', '77.61821530987529750213574367556', '77.99186738449059344650965078100', '78.61016100608650400430842745294', '79.71890018998097042625985399707', '79.948365457163992936154797984117', '80.62394570747244612038238701134', '81.07784207683402587396242120113', '81.476727385599100115778342799290', '82.45386857278550609253838014386', '82.82670947708701152296519332536', '83.16782230116147398880320588784', '83.736110066624453568849177231630', '84.44349757455860694243958618955', '85.11613024065115144767392015657', '85.93012432292150686120939336227', '86.231385823133238632283060381200', '86.760182573164401883888368515645', '87.3747084414098628781429869559', '87.97280208095188870165401052962', '88.44305739862366720089089840991', '88.76368340858960744988815493597', '89.73903204652489706898863103384', '90.1950723224790632910366614057', '90.5344847161889514087458774279', '91.476496738105747593939542593878', '91.94691792594894568987622486754', '92.63955281338633238233446725906', '93.19587212540664323489751047387', '93.33081830478749199090653015214', '93.97485669186612890458712391763', '94.794452928530117606596615926038', '95.07961467187030437415679758900', '95.76249480576178145182663214180', '96.564884484650054446224837395312', '96.89548434595867873787163186780', '97.622933960915884941686206497265', '98.06788010616644343963869603419', '98.8439854132648896959629438074', '99.2574151214487595878688525414', '99.624010640570690081661848977405', '100.15467963231988922815356339037', '100.77305386713507129422980767680', '101.50486765738368142330307660481', '101.86730224606717306167434573498', '102.85032491716232326147885900779', '103.120584322626243323890013214311', '103.790020423442830322077083579901', '104.13706030521773546688739282534', '104.88448753077976955438744858184', '105.38135152390845450343317570996', '105.84824679947408771231259494838', '106.418634592691868499887197201624', '106.80161990202579245995508472357', '107.59002431043641571079825151450', '108.199209545267058725260639489292', '108.99254245993861481930257246142', '109.31973730379547174496831407680', '109.80926488344079317952438570343', '110.355979809699213796662367394009', '110.7271938439842099023366215929', '111.67663044251910818490410165859', '112.082822920016642338099264500105', '112.36593811733145634441340105069', '112.89132392175602023369331561127', '113.88597192402955244690106850021', '114.45400440548405398209853771265', '114.90502611656612472231366525237', '115.28203876201134602917332771321', '116.06127469548441790549832639511', '116.49336493451750509531675220211', '116.89505497788674545547021953193', '117.4810324173639582148314425332', '117.98012126060087308772692572974', '118.77948661953417752121233063043', '119.29527742592537652261997290578', '119.72343010712747689297310718692', '120.44277522273494221474721921859', '120.941043241079125886490289888469', '121.66502931586421210089976837424', '122.023724637353862449406826476805', '122.401861772068366510767071896428', '123.10468442555597232264562041114', '123.30094998342703849671716853468', '124.33832093322527207905624632380', '124.736731516857652113249211961359', '125.341613395407510939934379059806', '125.94184829963527580358870461284', '126.38550861451695920232278568237', '127.098059449535953041984659303284', '127.56427072525752384674933687860', '127.95061337198375827827426755219', '128.608005030230524782676557059673', '128.98525544647065352766515440965', '129.80636832851166937865104110668', '129.873805829547614685146323288667', '130.94474294616692063250913892753', '131.522166792975355657903808344214', '131.97664067993305473825920100814', '132.47530525781420611656140110513', '132.88513879951187851458168350742', '133.56207682933045704944698430839', '134.03438651302707758470075333964', '134.63704914349503393441480598998', '135.12847612884266152029084676221', '135.49878284467916734443345996205', '136.161050519353969115212050297298', '137.00975179519715894967369666904', '137.44230173872577106044320037981', '138.011061331907974282715027204619', '138.49990102615602019589521258898', '139.026631832877750242916354212294', '139.32385848343024569073407813838', '140.02110633483326673921641845303', '140.715473683143307366034345941739', '141.01697952785111498060299831157', '141.65377919320153444472073236678', '142.190913550064758389000491852220', '142.89641305292810212560637809355', '143.52691941542788112385687241198', '143.9844285794739862082514009295', '144.40669237071893382061374926736', '144.89647930055002157116601889139', '145.61096607245975660840207882990', '145.88211756605865409923812684591', '146.48837104309785379804016637628', '146.96388799130351700684273758352', '147.86665598605238054879249929196', '148.31459687869775640023758578512', '148.852940578502440309187625888155', '149.1342984501244406646073654678', '150.06390137364431106130237217651', '150.49736530249497684539299668489', '150.83106319671970911996393236068', '151.51717754510263782030826723747', '151.847726966741876000928795643', '152.28274491723956882827740651058', '153.121665607706676827204456406302', '153.78526766621562474618207244712', '154.36856840974420820657797438067', '154.61296658913727889468063289336', '155.26974917935424850522613199917', '155.88908267018397618602475882681', '156.40319386910430114682473860364', '156.81372764936409330328684853424', '157.30989184109711161444319584906', '157.86483016996360983652509713872', '158.36982029616319523513955059540', '159.173281031774180695959941014922', '159.36680099710169501710248953145', '160.25854533201653203737150021797', '160.9946689691847950236862357219', '161.242136438404775800786545668921', '161.58244295384702507765246007472', '161.98597682959872174221308673992', '163.04965506287614668457019996349', '163.270598034931637537629629816462', '163.67560147017019318668084719229', '164.37599032308059025652574308067', '164.85710550013556116311115115075', '165.51022259593591909697038108800', '166.29619596725340830735411729423', '166.62611357436651891688310168144', '167.03572280154304508722722783041', '167.75810883535880231754005566836', '168.10747203482967740094114133417', '168.43264327376711989914664529187', '169.330265596294939870854261411677', '169.64458048045962792524196248884', '170.27134393653834594607996613147', '170.83190423446989367991218794808', '171.52805196040240356551234612696', '171.939333914564248936377966219773', '172.54751423786372291997059086091', '172.94670057458249513798658419270', '173.65597537815440382220513341342', '174.06291109951767622038221094766', '174.39625067413030911891707675282', '174.96051170722026408330409051229', '175.51007372212304282099180013514', '176.49453809702680610428016527641', '176.5556370250188822526565103308', '177.41378662238898350927924080526', '177.91834434225702522681716933028', '178.22105012123370046168474990325', '178.872118202518564786516239968940', '179.438619614159911740260905408713', '180.00258681634004295600992004644', '180.4012515596333143411792873910', '180.70742018856752917225838881215', '181.45870224258169449133890839210', '181.954794385515952814493316437406', '182.99849119105401447747519058168', '183.2687504308952144867227986129', '183.415317406674424179638319643533', '184.230052309799485923043110848839', '184.81295764710088058209434334593', '185.199203833901635341653945044209', '185.73221939640844000660394913905', '186.22608477100159387084612252496', '186.720357900768583905540931520639', '187.37509142056850351673020765853', '187.84946472037283778776861703226', '188.49277076798897465419766603979', '189.0798019657874341377571125', '189.63634458919598422096468516114', '190.14562652429309034571477524202', '190.52236490796550877071253588148', '191.011127171982597925771705873303', '191.33979289302560282468116098139', '192.25731610991187640173372934455', '192.70358893521422873216186406887', '193.10319339722956873935686025594', '193.63727419513851987415958964318', '194.36773814396108733135683677845', '194.90755001941945688779240792281', '195.504159042513971591207392848643', '195.85640870014675894991791379724', '196.448453593473251552603760086487', '196.69041379547762085231886957821', '197.45428356929895295571998520163', '197.87531594318592055240445386604', '198.37140633116578799779781974405', '199.00285830004479351605628795518', '199.71707034535141386299668772620'], 'prelabel': '1-4600-4600.3261-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.362310190967847, 'root_angle': 0.3100354615430764, 'root_number': '-0.368331708388877988322429441741+0.929694440445531839668454028868*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(110)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.01030557144508310599380769582+0.0145385843463256911760907480034*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.25283155559', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.97013959312', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.61658033306', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 21.362310190967847, 'bad_primes': [2, 5, 23], 'central_character': '4600.3261', 'conductor': 4600, 'conductor_radical': 230, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4600/3261'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-4600-4600.3261-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-4600-4600.3261-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.362310190967847, 'root_angle': 0.3100354615430764, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25283155559', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4600.3261', 'Lhash_array': ['dirichlet_L_4600.3261'], 'factors': ['1-4600-4600.3261-r0-0-0'], 'label': '1-4600-4600.3261-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4600/3261'}
Lfunction data - 1-4600-4600.3261-r0-0-0